DESIGN OF A HIGH LUMINOSITY 100 TeV PROTON -ANTIPROTON COLLIDER

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1 DESIGN OF A HIGH LUMINOSITY 100 TeV PROTON -ANTIPROTON COLLIDER A Dissertation presented in partial fulfillment of requirements for the degree of Doctor of Philosophy in the Department of Physics and Astronomy The University of Mississippi by SANDRA JIMENA OLIVEROS TAUTIVA April 2017

2 ProQuest Number: All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. ProQuest Published by ProQuest LLC ( 2017). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI

3 Copyright Sandra Jimena Oliveros Tautiva 2017 ALL RIGHTS RESERVED

4 ABSTRACT Currently new physics is being explored with the Large Hadron Collider at CERN and with Intensity Frontier programs at Fermilab and KEK. The energy scale for new physics is known to be in the multi-tev range, signaling the need for a future collider which well surpasses this energy scale. A cm 2 s 1 luminosity 100 TeV proton-antiproton collider is explored with 7 the energy of the LHC. The dipoles are 4.5 T to reduce cost. A protonantiproton collider is selected as a future machine for several reasons. The cross section for many high mass states is 10 times higher in p p than pp collisions. Antiquarks for production can come directly from an antiproton rather than indirectly from gluon splitting. The higher cross sections reduce the synchrotron radiation in superconducting magnets and the number of events per bunch crossing, because lower beam currents can produce the same rare event rates. Events are also more centrally produced, allowing a more compact detector with less space between quadrupole triplets and a smaller β for higher luminosity. To adjust to antiproton beam losses (burn rate), a Fermilab-like antiproton source would be adapted to disperse the beam into 12 different momentum channels, using electrostatic septa, to increase antiproton momentum capture 12 times. At Fermilab, antiprotons were stochastically cooled in one Debuncher and one Accumulator ring. Because the stochastic cooling time scales as the number of particles, two options of 12 independent cooling systems are presented. One electron cooling ring might follow the stochastic cooling rings for antiproton stacking. Finally antiprotons in the collider ring would be recycled during runs without leaving the collider ring, by joining them to new bunches with snap bunch coalescence and synchrotron damping. These basic ideas are explored in this work on a future 100 TeV proton-antiproton collider and the main parameters are presented. ii

5 DEDICATION To my parents for their loving support and encouragement during all these years of study away from home. To John Acosta, his company in all this time has been the motivation in my academic growth. iii

6 ACKNOWLEDGEMENTS I want to express my deepest gratitude to Dr. Donald Summers and my advisor Dr. Lucien Cremaldi for their helpful contributions to this work. Thanks for their guidance and valuable corrections to this work. Also, I want to thank Dr. Hailin Sang and Dr. Alakabha Datta for serving as members on my thesis committee and for their suggestions and comments about this work. iv

7 TABLE OF CONTENTS ABSTRACT ii DEDICATION iii ACKNOWLEDGEMENTS iv LIST OF FIGURES viii LIST OF TABLES xiii 1 INTRODUCTION LITERATURE REVIEW Standard Model The LHC CERN Proton-Antiproton Collider The Tevatron at Fermilab The Antiproton Source Antiproton Cooling RF Bunch Rotation Stochastic Cooling Antiproton Stacking Electron Cooling Beam Parameters in Particle Accelerators Synchrotron Radiation Magnetic Devices in Particle Accelerators v

8 2.7.1 Magnetic Dipoles Magnetic Quadrupoles Inner Quadrupole System for the Interaction Regions (IP) Quadrupole Matrix Formalism Lithium Lens Beam Separation Devices Radio Frequency Cavity Beam Simulation Programs PROTON-ANTIPROTON COLLIDER REMARKS Cross Section for Higher Masses in pp and p p Collisions Synchrotron Radiation in High Energy Colliders ANTIPROTON CAPTURE Luminosity Requirements Increase in Antiproton Momentum Acceptance Antiproton Beam Separation and Transport ANTIPROTON COOLING Debuncher-Accumulator Rings Debuncher Rings Electron Cooling System Recycling of Antiprotons in the Collider Ring COLLIDER DESIGN AND PARAMETERS Collider Layout Tunneling Main Dipole Magnets Parameter Calculation vi

9 6.5 Inner Quadrupole System CONCLUSIONS BIBLIOGRAPHY LIST OF APPENDICES A G4BEAMLINE CODE B MADX PROGRAM FILE VITA vii

10 LIST OF FIGURES 2.1 The Standard Model. Source: [6] The Large Hadron Collider LHC Fermilab s accelerator chain Antiproton Source. Antiprotons are generated in the target station, then enter the Debuncher through of the AP2 line and then are sent to the Accumulator ring to be finally extracted through of the AP3 line Fermilab Target Station Accumulator Lattice. Source: [12] RF Bunch Rotation. (a) A bunch with large energy spread is injected. (b) The bunch starts rotating in phase space. (c) The RF voltage is reduced and starts the adiabatic debunching. (d) The bunch rotation is complete when the energy spread reduction is complete Model of Stochastic Cooling Cooling and heating effects in terms of the system gain [18] Stacking Process. (a) The first bunch is injected. (b) The bunch is moved to the stack region. (c) A second bunch in injected 2.2s later. (d) The second bunch is moved to the stack region. (e) After successive bunch injections a dense core is formed in the stack Antiprotons density distribution in the stacking process for the accumulator ring Accumulator Cooling Systems. Figure adapted from [12] Principle of electron cooling. The high energy spread of the antiprotons is reduced when they are injected into a cooling section to interact with electrons with low energy spread viii

11 2.14 Phase space of a beam with the form of an ellipse. The coordinate u represents the position x or y Magnetic Dipole. Source: [25] A Dipole bends particles according to their momentum Magnetic quadrupole. Source: [25]. The magnetic field is proportional to the radial direction and is zero at the center Magnetic focusing and defocusing quadrupole Quadrupole FODO Cell. A focusing (F) and defocusing (D) quadrupole separated by a drift space Inner quadrupole system to provide the final focusing for the collision of the particle beams Inner triplet quadrupole scheme for CMS and ATLAS Inner triplet quadrupole scheme for the Tevatron (Fermilab) Initial vector coordinates (x 0, x 0) entering a lens and final vector coordinates (x 1, x 1) leaving the lens A lithium lens collecting particles and orientating them horizontally Beam deflection produced by an electric septa Electrostatic septum used to extract one part of the beam [26] DC Magnetic Septum. The beam is separated into two parts, one enters in the field region B and the other part continues without change in the no field region Radio Frequency Cavity. Source: [28] Electric and magnetic fields in a cavity. The electric field accelerates or decelerates the particles according to their arrival time Simulation example in G4beamline. A flat beam goes through two quadrupole magnets which focus the beam in a specific region [30] MAD -X Betatron Function Plot for the CMS Interaction Region ix

12 3.1 Cross sections in term of the mass for the Higgs production at E cm =7 TeV [41] Top-like Anti-top-like Cross section production as a function of the mass using pp and p p collisions [39] Feynman Diagrams for W production from a) q q collision, b) qq collision MadGraph results for W Boson production cross section as a function of the mass using pp and p p collisions with a E cm = 100 TeV Pythia results for W Boson production cross section as a function of the mass using pp and p p collisions with a E cm = 100 TeV Momentum distribution of the antiprotons produced by a 120 GeV proton beam hitting a tungsten target [51] GeV/c± 2% antiproton beam simulation crossing a lithium lens. The plots show the transverse momentum distribution of the beam before entering (left plot) and in the output of the lithium lens (right plot) GeV/c ± 24% antiproton beam simulation crossing a lithium lens in G4beamline. The plots show the transverse momentum distribution of the beam before entering (left plot) and in the output of the lithium lens (right plot) Momentum vs x position for the initial beam (left plot) and the dispersed beam (right plot) Configuration to divide the beam into two parts. An initial beam with momentum acceptance p = 11.0 GeV/c ± 24% is collected by the Li lens and dispersed by a magnetic dipole to be then divided by a electrostatic septa ES and two magnetic dipoles MS Momentum distribution of the initial beam (upper plot) and when it is divided into two (bottom plot) An initial beam with momentum acceptance p = 11.0 GeV/c ± 24%is divided to finally get twelve beams Momentum distribution of the beams 1, 2 and Momentum distribution of the beams 4, 5 and Momentum distribution of the beams 7, 8 and x

13 4.11 Momentum distribution of the beams 10, 11 and To cool 12 more antiprotons, 12 independent cooling systems would be implemented. Two accumulator rings can keep up with one p/h Debuncher output rate independent cooling systems using only Debuncher rings. Alternatively, bunch coalescing might be done with electron rather than stochastic cooling Antiprotons are sent alternatively from the target to each Debuncher to increase the cooling time from 2.2 to 4.4 s, allowing emittance (RMS, Normalized) reduction from 330 to 3 µm Fermilab Electron Cooling System [59] Electric fields at the beam pipe center and wall of a circulating beam Snap Bunch Coalescing. (a) A group of bunches are centered at low frequency and their momentum spread is reduced. From (b) to (c) the bunches are rotated for 1/4 of a synchrotron oscillation period at low frequency and then captured at high frequency. The momentum spread increases and the bunches are captured in a single bucket TeV proton-antiproton collider (not to scale). An intermediate energy ring between 120 GeV and 22 TeV is not shown. Bunch stacking in the single electron cooling ring might replace the 24 Accumulator rings. A bit of additional transverse cooling would have to be coaxed out of the Debuncher rings to allow electron cooling Possible scenario to construct the 270 km ring in Illinois connected to Fermilab. An engineering study has been done for a 233 km ring at Fermilab [79, 80]. Map data: Google Layout of the 270 km ring around Dallas, Texas [83]. Map data: Google km tunnel to host a 100 TeV pp collider at CERN in the Lake Geneva valley. Image credit: CERN LHC Main Dipole Magnet. There are two cosθ layers [87] T superferric dual bore dipole magnet [5]. A p p collider would only require one bore xi

14 T superferric dual bore dipole magnetic design [5]. A p p collider would only require one bore Beta function plots for the D0 Experiment interaction region Beta functions plots for the 100 TeV p p collider interaction region. A combination of quadrupoles focus the beam in the IP with β* = 14 cm xii

15 LIST OF TABLES 2.1 Parameter list for Tevatron and LHC Colliders Longitudinal emittance damping time for Tevatron and LHC Colliders Synchrotron Radiation (SR) for a 100 km pp and 270 km p p circumference colliders. γ = E/m = 53, TeV beam energy Parameters of the basic cell to divide the initial beam Mean momentum value of the 12 beams obtained Fermilab antiproton cooling stages [54]. The normalized rms emittance shown comes from multiplying geometric rms emittance by β γ = p/m = 8.9/0.938 = A modest amount of stochastic cooling is performed in the Recycler ring to prepare for electron cooling in the same ring Electron Cooling System Main Parameters Electron Ring Main Parameters Comparison between tunneling cost for three different locations considered for a 270 km collider ring [85] Tunneling-time estimate Main Dipole Magnets for the 270 km collider ring Parameter list for the Tevatron, the LHC, the Future Circular Collider FCChh, and the 100 TeV p p proposed here Inner Triplet Quadrupole parameters xiii

16 CHAPTER 1 1 INTRODUCTION With the recent discovery of the Higgs boson the standard model of particle physics is complete, but exploration will continue to search for beyond the standard model (BSM) physics that many agree must exist. The CMS and ATLAS experiments at the LHC (Large Hadron Collider) observed a Higgs boson with mass of about 125 GeV, using a data sample with collision energies of 7 and 8 TeV [?, 2]. The LHC started taking data at 13 TeV in 2015, and it will continue increasing the number of collisions. The LHC reached its design luminosity of cm 2 s 1 in June The second most powerful hadron collider was the Tevatron at Fermilab. This collided protons and antiprotons with a center of mass energy of 1.96 TeV. During its 28 years of operation (closing in 2011) one of its greatest discovery was the top quark in 1995 [3, 4]. Currently Fermilab experimenters will continue analyzing previous data and new particle research projects are under development. Among them are new high intensity neutrino and muon decay experiments. Many agree that hadron colliders beyond 14 TeV are necessary to fully explore new BSM physics. For that reason, some projects are being carried out, as for example, a 100 TeV proton-proton collider in a 100 km ring with 16 T Nb 3 Sn dipoles is being considered for CERN. Synchrotron radiation in the dipoles, 16 T fields, and detector pileup are concerns. The design is challenging. Might a simpler hadron collider be possible? This is the motivation to consider the construction of a high energy proton-antiproton (p p) collider. The center of mass energy considered would be 100 TeV with a luminosity of cm 2 s 1, and would use 4.5 T NbTi superferric dipoles [5] in a 270 km tunnel. Much of the technology for this 1

17 collider is available and was demonstrated at the Tevatron (L = 4 x cm 2 s 1 ). The most important factor in the study of a 100 TeV p p machine would be to find a way to cool and recycle more antiprotons to achieve higher luminosity. The main literature review of this work is presented in chapter 2, mainly about the Tevatron antiproton source and some concepts in accelerator physics. In chapter 3, we present the important advantages of a high energy(he) p p collider with respect to a HE pp collider. Cross sections for the production of many high mass objects are much larger in p p collisions. Calculations and results are shown and compared for both types of colliders. Furthermore, advantages deduced from these calculations are discussed. In chapter 4 we discuss some important aspects in achieving higher luminosities with proton-antiproton colliders. Among those is, increased momentum acceptance in a Fermilablike antiproton source to get more antiprotons and the separation of them into 12 different momentum channels. Chapter 5 is dedicated to the cooling of the antiprotons. This process is important to control the random motion of the particles and beam emittance. Also, because 12 times more antiprotons are needed, twelve independent cooling systems are proposed. One option uses Debuncher and Accumulator rings and a second option uses only Debuncher rings. Finally, an electron cooling ring would follow either of the two cooling system options. Chapter 6 focuses on the final collider parameters together with relevant calculations. We discuss the beam optics necessary to achieve lower values of β for achieving higher luminosity. Finally in chapter 7 the conclusions of this work are presented. 2

18 CHAPTER 2 2 LITERATURE REVIEW 2.1 Standard Model The standard model of particle physics is based on fundamental particles called fermions and bosons. Fermions are spin 1/2 particles which include quarks and leptons. Bosons are particles having integer spin, including the fundamental force carriers: the photon, the W and Z bosons, the gluon, and the Higgs boson. The structure of the standard model is shown in Fig. 2.1, where it is observed that the fundamental quarks and leptons form a fermion group and the force carrying bosons together with the Higgs form the boson group. Figure 2.1. The Standard Model. Source: [6] Looking more closely, there are six types or flavors of quarks grouped by generations. The quarks, up and down, belong to the first generation which are the most stable 3

19 and least massive. For the second generation we have the quarks, charm and strange, and the third one the quarks, top and bottom, which are more massive. The quarks cannot exist alone, thus a quark and antiquark form the mesons (pion π, kaons K, eta η, rho ρ, omega ω, phi φ, etc.). The combination of three quarks qqq (or antiquarks q q q) form the baryons. These are massive particles, among which are the proton p and neutron n. Other baryons are the lambda (Λ), sigma (Σ), delta ( ), chi (ξ), and omega(ω). The individual quarks have fractional electric charge, ±e/3 or ±2e/3, but they combine to form hadrons (mesons and baryons) which have integer charge as they hadronize. The leptons are classified by generation, in which the electron, e, has the least mass and the tau lepton, τ, the greatest mass. The muon, µ, and the tau are unstable particles with a lifetime of 2.2 µs and 0.29 ps, respectively. The electron, muon, and tau each have an associated neutrino, ν e, ν µ, ν τ. These neutrinos have no charge and their masses are slightly above zero. Neutrinos interact with matter through the weak interaction. Five particles form the group of the gauge bosons: the gluon, photon, W, Z, and the most recent Higgs boson. These gauge bosons are the force-carrying particles. The gluon is the mediator of the strong force, which binds protons and neutrons together inside the nucleus. The photon mediates the electromagnetic force which acts between charged particles; for example, it binds electrons to the nucleus. The weak force, which describes β-decay, is carried by the bosons W and Z. 2.2 The LHC The Large Hadron Collider (LHC), Fig. 2.2, is a circular accelerator of 27 km circumference located 100 m underground near Geneva, Switzerland. It was built by CERN (European Organization for Nuclear Research) in order to explore new physics at the energy scale of the order of 14 TeV. It is designed for proton-proton collisions. The protons are accelerated in groups of 1.15 x interacting every 25 ns from opposite directions at the interaction point (IP). There are about proton-proton inelastic collisions at the IP each 4

20 25 ns and a few high transverse momentum interactions, possibly with high mass particles. Its biggest goal was the search of the Higgs Boson, a particle that plays a fundamental role in the Standard Model of elementary particle physics. Figure 2.2. The Large Hadron Collider LHC. At the LHC the injections chain starts with a proton linear accelerator that accelerates protons to an energy of 50 MeV. The Proton Synchrotron Booster (PSB) accelerates the protons to the energy of 1.4 GeV. The particles are then injected in to the Proton Synchrotron (PS), which produces proton bunches with 25 ns spacing. From there they are directed to the 6.9 km Super Proton Synchrotron (SPS) ring where they are accelerated to an energy of 450 GeV. Finally two proton beams (2808 bunches each) are injected into the 27 km LHC 5

21 ring to be accelerated to an energy of 7 TeV in opposite directions. The LHC ring uses two pipes, one for each beam. Four experiments, CMS, ATLAS, LHCb and ALICE, are located at the four interaction points of protons. The CMS and ATLAS experiments are of general purpose type and their objective is to explore the limits of the Standard Model. LHCb and ALICE are smaller experiments. The LHCb experiment focuses on bottom quark (b) physics and ALICE focuses on heavy ion physics CERN Proton-Antiproton Collider The Super Proton Synchrotron (SPS) was used as a p p collider [7]. From the SP ring a 26 GeV proton beam hit a Cu target, from which antiprotons are created. For each proton beam (10 23 protons) around antiprotons were created. Only those with momentum p = 3.5 GeV/c ± 1.5% were selected, which is the SPS momentum acceptance. The first collisions were observed in 1981 with a 0.55 TeV collision energy. Then, in 1982 the W boson was discovered [8, 9], and with an increase in luminosity the Z boson was discovered in 1983 [10,11]. Its last run occurred circa 1989 in time for CERN to begin building the Large Electron Positron Collider, LEP. However, CERN still produces antiprotons for antimatter experiments. 2.3 The Tevatron at Fermilab The Tevatron was the largest circular proton-antiproton collider built to date. In 1985 its first proton-antiproton collisions with a center of mass energy E cm of 1.6 TeV were produced. The Tevatron finished operations at the end of September in 2011 with E cm of 1.96 TeV. One of its greatest discovery was the top quark in The Tevatron accelerator chain of components (Fig. 2.3) are the Cockcroft-Walton Accelerator, in which hydrogen gas is ionized to H and accelerated to 750 kev, the Linac (Linear accelerator), where the H ions are accelerated to an energy of 400 MeV. Then, they pass through a thin carbon foil, which removes the electrons leaving only protons. The Booster (circular accelerator) accelerates the protons to 8.9 GeV in 20,000 revolutions. Then, 6

22 the accelerated protons enter the Main Injector, where some are accelerated to 150 GeV to be injected into the Tevatron. The remainder are accelerated to 120 GeV and sent to the antiproton source, where the antiprotons are produced. In the Main Injector, the protons and antiprotons are accelerated to 150 GeV and injected into the Tevatron. There, protons and antiprotons are accelerated until they reach an energy of 0.98 TeV per beam prior to collision. In the Tevatron the proton and antiproton beams are collided at the CDF and D0 detectors. Figure 2.3. Fermilab s accelerator chain The Antiproton Source The antiproton source consists of four parts (Fig. 2.4), the target station and three storage rings: the Debuncher, the Accumulator, and the Recycler (not shown in the figure). 7

23 In the target station, Fig. 2.5, around antiprotons of energy 8.94 GeV (peak Booster energy) are created every 2.2 s by hitting the 8 cm long nickel target with a beam of protons (120 GeV) coming from the main injector. Then a lithium lens (the least dense solid conductor) is used to horizontally and vertically focus the particles into a beam line, acting like magnetic quadrupoles. Using a pulsed magnet the particles are separated according to their charge. The negatively charged particles are mainly antiprotons and pions. The remaining particles are absorbed by a graphite-core beam dump. The antiprotons production rate depends on the proton beam energy. The antiproton collection efficiency (from the target) is greater if the proton beam spot size on the target is reduced. Figure 2.4. Antiproton Source. Antiprotons are generated in the target station, then enter the Debuncher through of the AP2 line and then are sent to the Accumulator ring to be finally extracted through of the AP3 line. The Debuncher is a 500 m round triangle storage where the antiprotons are collected from the target station. It is divided into 6 sectors, which contain 19 quadrupole magnets, 11 dipoles, a system of correction dipoles to control the beam and a system of sextupoles for chromaticity control. In the Debuncher the momentum spread of the 8.9 GeV/c antiprotons 8

24 is reduced using RF bunch rotation. The Debuncher supplies around p/h to the Accumulator. From the Debuncher the 8.9 GeV/c antiprotons are sent to the Accumulator. Figure 2.5. Fermilab Target Station. The Accumulator, Fig. 2.4, is a 474 m rounded triangular shape (6 straight sections and 6 flattened corners) designed to store, cool, and stack the antiprotons. In the arc sections the dispersion (beam separation according to its momentum) is large ( 9 m), and the straight sections have low and high dispersion. Fig. 2.6 shows a lattice of the Accumulator, which represents one sector of the six, where 14 quadrupoles (QF, QD), 5 sextupoles, 5 dipoles, and other devices are located. In the sectors A10 and A20 are located the cooling systems. In the Accumulator the antiprotons are stacked and cooled using a cooling process called stochastic cooling; this method will be explained in the next section. The maximum stack of antiproton into the Accumulator is 150 x It supplies around p/h to the Recycler. The transfer time of antiprotons from the Accumulator to the Recycler is 30 minutes. The Recycler is an 8.9 GeV/c storage ring located in the main injector tunnel, on the top of the Main Injector Ring, with the same circumference (3.32 km). In the Recy- 9

25 Figure 2.6. Accumulator Lattice. Source: [12]. cler Ring there are approximately 344 permanent magnets, which provide bending and 100 permanent quadrupoles to perform optical focusing. Its initial purpose was to recycle the 10

26 unused antiprotons from the collisions, as well as to accumulate large quantities of antiprotons (around ) [13]. However, the recycler proved not to be effective in recycling antiprotons and therefore it was never used for that purpose. But it was useful for storing and cooling antiprotons. In the scheme more antiprotons can be stored prior to collision, increasing luminosity. With this new ring the number of stored antiprotons was increased to x p. The antiprotons are stored for about 15 hours and then sent to the Main Injector. The storage efficiency of 93% is determined by the loss in injection and extraction processes (4%) and by of the antiproton beam lifetime (3%). In the Recycler the antiprotons are initially cooled by stochastic cooling and then by electron cooling. These cooling systems are explained in the next section. 2.4 Antiproton Cooling The cooling process in a beam is very important to its quality, allowing the collision of beam bunches. The cooling process consists of reducing the random motion of the beam or its phase space volume. Several types of beam cooling are in use. The random motion of antiprotons can be reduced by stochastic and electron cooling. Cooling by synchrotron radiation damping is used for electron and positron storage rings [14]. Laser cooling [15] is used for ions and ionization cooling [16] can be used for muons RF Bunch Rotation In this process a bunch of antiprotons, initially with large energy spread, is rotated (90 ) in phase space reducing the energy spread through RF voltage manipulations [17], as seen in the Fig This technique is used in the Debuncher ring to reduce the momentum spread of the antiprotons from 2.25% to 0.1%, which it takes around 60 ms. The rest of the time (2.2s), the antiprotons are cooled through stochastic cooling to reduce the RMS Normalized emittance from 330 to 30 µm. Longitudinal stochastic cooling is employed as well. The Debuncher Ring is called the debuncher because the small bunch momentum spread comes at the cost of longer bunches. 11

27 Figure 2.7. RF Bunch Rotation. (a) A bunch with large energy spread is injected. (b) The bunch starts rotating in phase space. (c) The RF voltage is reduced and starts the adiabatic debunching. (d) The bunch rotation is complete when the energy spread reduction is complete Stochastic Cooling The stochastic cooling principle was initiated by Simon van der Meer in He received a Nobel Prize in 1984 for his work. The cooling consists of reducing the transverse size, transverse angles, the longitudinal size, and the momentum spread ( p/p) of a particle beam, with minimal beam loss. The relative velocity of the particles with respect to each other in a bunch is reduced. Stochastic cooling covers both betatron and momentum cooling. Betatron (or transverse) cooling refers to the reduction of the betatron oscillation in the horizontal and vertical transverse planes, while momentum cooling refers to the reduction in momentum spread of the particles in the beam. In these processes, particles can be 12

28 considered as points with some empty space between them allowing conservation of density in small scale [18]. For this reason the Liouville theorem [19], which states the phase space density must remain constant, would not be violated. Stochastic cooling is a not conservative process. Kickers can cool a bunch as long as the number of particles is finite. Figure 2.8. Model of Stochastic Cooling. Fig. 2.8 shows the main basic principle of stochastic cooling, where a pickup (array of electrodes within a vacuum tank) is used to identify the position of the particles. Then this signal is amplified and sent to the kicker, which corrects the motion of particles reducing its betatron oscillation using an electric field. This process is repeated many times to cool the beam. The pickup and the kicker are separated by a odd number of quarter betatron wavelengths λ in order to cancel any oscillation. In practice, the signal will overlap due to the large quantity of particles, but the perturbing effect (heating) is zero on average. In the Accumulator, in the low dispersion sections, it is convenient to place the pickup system for betatron cooling, while in the high dispersion region the pickup system is suitable for momentum cooling. To determine the cooling time, consider N particles in the ring, the signal arriving at the kicker depends on W, which is the bandwidth of the cooling system 13

29 (up to 8 GHz). The cooling rate, which is the inverse of cooling time, is given by 1 τ = W 2N (2.1) Here we have that the cooling time scales in proportion to the number of particles. Now, taking x as the offset to the test particle, the correction in the kicker is λx, where λ is related to the amplification of the system. The corrected position received from the kicker [20] is x = λx λx i (2.2) where the second term of the right side refers to the other particles excluding the test particle. The average sample error x s = 1 N s xi (2.3) then x can be written as x = g x s (2.4) Here g = N s λ is called the gain. This shows how the cooling system applies a correcting kick by measurement x s. Another important parameter considered in the cooling system is the mixing factor M, (M 1, with M = 1 being the perfect mixing) which is related to the heating effect due to the other particles. The thermal noise factor, U =noise/signal, is related to the amplifier system. In terms of these variables, the stochastic cooling rate [18] can be calculated using equation 2.5. If g<1, and g = 1/(M + U) is the optimum system gain to get fastest cooling. However, the maximum cooling rate (W/N) is obtained if the gain is g = 1, zero noise U = 0, and perfect mixing M = 1. 1 τ = W 2N (2g g2 (M + U)) (2.5) An optimum gain can be determined in order to have more cooling and less heating. This is 14

30 shown in Fig. 2.9, where the cooling effect is directly proportional to the gain while the heating effect is corresponding to g 2. There the optimum gain is the point where the difference between the cooling rate and the heating rate is greatest. Stochastic cooling is applied in the Figure 2.9. Cooling and heating effects in terms of the system gain [18]. Debuncher (in addition to Bunch Rotation) and accumulator rings. In the Debuncher the beam size is reduced by decreasing the transverse emittance (RMS Normalized) from about 330 to 30 µm. The antiprotons are next sent to the Accumulator ring. There, additional stochastic cooling is used, where the transverse emittance (RMS Normalized) is reduced to 15 µm, together with RF manipulations to accumulate p/h. This amount is transferred to the Recycler every 60 minutes Antiproton Stacking To optimize the collection of antiprotons in the accumulator ring, a stacking process is carried out using stochastic cooling. This is shown in Fig The first antiproton group coming from the Debuncher ring is injected into the Injection orbit. Then this group is moved to the Stack region by decelerating the antiprotons using an RF system. 2.2 seconds later the next bunch is injected and the same procedure is repeated. After one hour all the bunches in the stack form a dense core and the extraction process takes place. Fig

31 Figure Stacking Process. (a) The first bunch is injected. (b) The bunch is moved to the stack region. (c) A second bunch in injected 2.2s later. (d) The second bunch is moved to the stack region. (e) After successive bunch injections a dense core is formed in the stack. Figure Antiprotons density distribution in the stacking process for the accumulator ring. shows the density variation in each region of the stacking process as well as the momentum cooling, which is greater in the core region. Additional stochastic cooling, momentum and transverse, is done in this region. 16

32 In the Accumulator, the cooling system is distributed as is shown in Fig The pickups for stacktail cooling are located in the zone A60 together with the pickups for core 2-4 GHz momentum cooling, while in the zone A30 are found the kickers for these systems. Similarly, in the zone A10 we can find the pickups for core 2-4 GHz and core 4-8 GHz betatron cooling and in the zone A30 also the kicker for these systems. Finally, for core 4-8 GHz momentum cooling the pickups are in the zone A20 with their corresponding kickers located in the zone A50. Figure Accumulator Cooling Systems. Figure adapted from [12] Electron Cooling Electron cooling is based on the heat exchanger basis through the Coulomb interaction between a high energy spread (antiprotons or ions) beam and a low energy spread electron beam. See Fig In this cooling process the circulating electron beam has the same average speed as the antiproton beam, which transfers energy to the electron beam, reducing its energy spread. Maximum cooling is reached when the temperature of the two beams are equal. An important characteristic of the electron cooling process is the high efficiency for 17

33 low energy beams. The cooling time [20] is independent on the number of antiprotons, but is directly proportional to γ 2, τ = γ 2 Mu 3 4πηm e Z 2 r 2 ec 4 ρ L L C (2.6) where M is the ion mass, u the velocity of the ion, η=cooling section length/ring circumference, m e the electron mass, Z the ion charge number, c the speed of light, ρ L the electron beam density, and L C is a constant factor (Coulomb Logarithm) for the cooler, on the order of 10. Figure Principle of electron cooling. The high energy spread of the antiprotons is reduced when they are injected into a cooling section to interact with electrons with low energy spread. In the Recycler ring the antiprotons are initially cooled using stochastic cooling. The antiproton and electron speeds must be close for electron cooling to work. Electron cooling follows stochastic cooling. Electron cooling was implemented at Fermilab in The cooling section is 20 m long inside the Recycler, and there a 4.3 MeV electron beam is used to cool the 8.9 GeV/c antiprotons transversely and longitudinally. The Recycler accumulated about antiprotons (with a 200 h lifetime) thanks to the use of electron cooling, which contributed to the overall Tevatron luminosity improvement by a factor of 25%. 18

34 2.5 Beam Parameters in Particle Accelerators In a particle accelerator, the energy and the luminosity are the most important parameters. Higher masses can be produced if the collision energy is greater. The luminosity is defined as the number of particles per unit of area and time in a collision. Its units are usually expressed in cm 2 s 1. The luminosity (equation 2.7) depends on the revolution frequency f 0, the number of bunches per beam N B, the number of particles per bunch N 1 (beam 1), N 2 (beam 2), the beam sizes σ x and σ y. L = f 0N B N 1 N 2 4πσ x σ y (2.7) The beam size can be expressed in terms of the emittance ε, and the β function. The parameter emittance refers to the beam quality, and is related to the beam size and the area of the phase space ellipse (u, u ). In Fig. 2.14, we show the phase space of a beam of area πε x,y. It is common to use the term normalized emittance (ε N(x,y) ), which is equal to the geometrical emittance (ε x,y ) multiplied by the relativistic parameter β γ. The parameter β x,y is the optical beta function. β* is the betatron function at the interaction point. The beam size σ x,y can be calculated using the equation 2.8, where ε N(x,y) is the normalized transverse emittance, β rel =p/e and γ=e/m is the Lorentz gamma factor. σ x,y = βε N(x,y) β rel γ (2.8) In terms of these parameters, equation 2.7 for the luminosity [21] can be written as: L = γf 0N B N 1 N 2 4πε N(x,y) β (2.9) Considering that the beam is a group of charged particles, when two beam collide, the electromagnetic fields generated by each beam affects the other beam, producing a defocusing force in the transverse direction. This force makes the particles experience a tune shift. The 19

35 Figure Phase space of a beam with the form of an ellipse. The coordinate u represents the position x or y. number of betatron oscillations per turn is called tune. The beam-beam tune shift per collision is given by, ξ = Nr 0 4πε N (2.10) Here, N is the number of particles in the bunch, r 0 is the classical radius of the particle, and ε N the normalized emittance. For example, the beam-beam tune shift for the LHC, with N = particles/bunch, the classical radius of proton r 0 = m and the normalized emittance ε = 3.75 µm-rad, is ξ = In Table 2.1 some luminosity and beam parameters for the Tevatron [22] and LHC are shown. Also, an important parameter that can be calculated using the luminosity is the event rate of a collider, R = σl (2.11) where σ is the corresponding total cross section. For example, for the LHC the total cross 20

36 section at E cm = 14 TeV is about 110 mb. Thus, with L = cm 2 s 1 the event rate is s 1. Table 2.1. Parameter list for Tevatron and LHC Colliders. Collider Parameters Tevatron LHC Unit Luminosity (L) 3.4 x x cm 2 s 1 Energy Center of Mass (E cm ) TeV Circumference (C) km Collision Frequency (f) MHz Lorentz Gamma Factor (γ) Number of Bunches (N B ) Number of Protons/Bunch (N p ) 29 x x Number of Antiprotons/Bunch (N a ) 8 x Normalized RMS Transverse Emittance (ε N ) µm Betatron Function at IP (β ) m Beam Size at IP (σ) µm 2.6 Synchrotron Radiation Relativistic charged particles moving along a curved trajectory emit synchrotron radiation due to the transverse acceleration. The power emitted per particle is given by the equation [23], P = c q 2 (βγ)4 6πɛ 0 ρr (2.12) where ɛ 0 = F/m, q = C, ρ is the curvature or bend radius, which can be calculated using equation 2.17 (next section), and R is the ring radius. Now, the energy loss per turn (per proton), is E[T ev ]4 U 0 (kev ) = 7.6 ρ[m] (2.13) where E is the particle energy. Damping originates in lost energy in synchrotron radiation, which decreases particle momentum in the direction of its motion. Faster particles lose more energy. The longitudinal damping time, the time for a particle of energy E to radiate that 21

37 energy, is given by, τ ɛ = 2E 0T 0 J ɛ U 0 (2.14) where E 0 is the particle s energy, T 0 the orbit period (2πR/c), J ɛ the damping partition number (2 for J ɛ, 1 for J x and J y ) and U 0 the energy loss per turn [24]. For colliders it is more usual to use the term longitudinal emittance damping time, which is half of the longitudinal amplitude damping time. In Table 2.2 we show some parameters together with the longitudinal emittance damping time calculations for the Tevatron and LHC. Table 2.2. Longitudinal emittance damping time for Tevatron and LHC Colliders. Collider E beam (TeV) B (T) ρ (km) U 0 (kev) T 0 (s) τ ɛ (h) Tevatron x LHC x Magnetic Devices in Particle Accelerators Superconducting magnets are used to transport and control the size of the particle beam in an accelerator. The magnets perform no linear acceleration, where Radio Frequency (RF) cavities are used instead Magnetic Dipoles Among the magnet categories used in accelerators is the dipole, which is composed of a north and south pole separated by a distance producing a constant magnetic field inside as is shown in Fig A magnetic dipole is used to bend particles and produce dispersion. Mathematically the dispersion D(s) is defined as D(s) = x(s) p p (2.15) 22

38 Figure Magnetic Dipole. Source: [25]. where x(s) is the displacement due to the momentum spread, p the momentum acceptance and p the central particle momentum. A dipole spreads the particles according to their momentum, thus particles with higher momentum will be have a smaller deflection than particles with low momentum when passing though a dipole as is shown in Fig From the magnetic part of the Lorentz force F = q(v B), the bending radius ρ of the charged particle trajectory is given by, ρ = p qb (2.16) or in a more convenient form, ρ[m] = p[gev/c] 0.3B[T ] (2.17) Now, with the magnetic field in the y direction and the particles moving along the z axis, the deflection angle θ p/p, where p is the transverse momentum variation. This can be written as, θ = p t p t z z = 1 F dz (2.18) pv Integrating the previous expression in terms of the dipole length l, θ = F l pv = qbl p (2.19) 23

39 where the force F = qvb was written in terms of the magnetic field, with B perpendicular to v. This expression can be expressed in a more appropriate form by multiplying it by c (the speed of light) and using electron-volts units for p to cancel the q term. Then we have finally the expression, B[T ]l[m] θ x [rad] = 0.3 p[gev/c] (2.20) where the term 0.3 comes from the ratio between the speed of light value and the equivalence of 1 GeV to 10 9 ev. Figure A Dipole bends particles according to their momentum Magnetic Quadrupoles Another very important magnet used in particle accelerator is the quadrupole. A magnetic quadrupole, Fig. 2.17, consists of 4 magnets where the magnetic field grows in the radial direction, B z = G x B x = G z (2.21) where G is the quadrupole gradient. Its units are T/m. Another important parameter for a quadrupole is the magnetic strength k given by, k[m 2 ] = 0.3 G[T/m] p[gev/c] (2.22) 24

40 the quadrupole focal length f is related with k and the quadrupole length l by, f = 1 kl (2.23) Generally, when f >> l the quadrupole can be considered as a thin lens. Quadrupoles Figure Magnetic quadrupole. Source: [25]. The magnetic field is proportional to the radial direction and is zero at the center. have the characteristic of focusing in one plane and defocusing in the other. A focusing quadrupole focuses in the horizontal plane and a defocusing quadrupole focuses in the vertical plane. Fig shows these types of quadrupoles. To convert a focusing quadrupole Figure Magnetic focusing and defocusing quadrupole. 25

41 into a defocusing quadrupole and vice versa it is only necessary to rotate it 90 degrees. A quadrupole system provides the final focusing of the particle beams before collision by alternating focusing and defocusing. A FODO cell as is shown in Fig can be used to transport the beam. FODO refers to focus, drift, defocus, drift. Figure Quadrupole FODO Cell. A focusing (F) and defocusing (D) quadrupole separated by a drift space. Quadrupoles also produce the aberration chromaticity with the quadrupole focal length depending on the momentum. To correct or control this chromaticity one often uses sextupoles, which allow stronger focusing of higher momentum particles Inner Quadrupole System for the Interaction Regions (IP) In a particle collider, a quadrupole triplet system provides the final focusing of the particle beam to bring them to a collision point. A basic configuration is shown in Fig A symmetric combination of focusing and defocusing quadrupoles is placed in each side to provide the collision or interaction point, IP. The focal length of the triplet is the distance from the center of the quadrupole triplet system to the IP, L f = L + l 1 + a 1 + l (2.24)

42 where L is the distance from the interaction point to the quadrupole Q1. Fig shows Figure Inner quadrupole system to provide the final focusing for the collision of the particle beams. a scheme of the inner quadrupole system corresponding to the interaction region of the LHC, such as the IP where the CMS detector is located. These quadrupoles have a field gradient of 205 T/m and aperture diameter of 70 mm. Similarly in Fig a scheme for Figure Inner triplet quadrupole scheme for CMS and ATLAS. Figure Inner triplet quadrupole scheme for the Tevatron (Fermilab). the Tevatron inner quadrupole system is shown, which has a field gradient of 141 T/m and aperture diameter of 88.9 mm. There the quadrupoles are smaller in length, as well as a smaller IP distance with respect to the first quadrupole (Q4). 27

43 Quadrupole Matrix Formalism The differential equation that describe the particle trajectory in quadrupoles has the form u + K(s)u = 0 (2.25) where u can be either the position x or y, and s is the longitudinal position. For the plane, with bending, K = k + 1/ρ 2, where ρ is the bending radius and k the quadrupole strength. For the plane with no bending, K = k. In beam dynamics, the transfer matrix M describes the transformation between the position u and angle u in one point with respect to another initial point (u 0, u 0) as is shown in Fig for the coordinate x. u = M u 0 u u 0 Figure Initial vector coordinates (x 0, x 0) entering a lens and final vector coordinates (x 1, x 1) leaving the lens. For a focusing quadrupole the transfer matrix M is written as M QF = cos( 1 Kl) K sin( Kl) Ksin( Kl) cos( Kl) 28

44 where l is the quadrupole length. For a defocusing quadrupole the transfer matrix M is written as M QD = cosh( 1 Kl) K sinh( Kl) Ksinh( Kl) cosh( Kl) Now, for a drift space the matrix M is M Drift = 1 s 0 1 where s is the length of the drift space. Now, in thin lens approximation (l = 0),the transfer matrices are: M QF = 1 0 M QD = 1 0 M Drift = 1 s f f 1 In the case that focal length of the focusing and defocusing quadrupoles are the same f, we have that for a FODO cell (Fig. 2.19) the transfer Matrix is given by, M F ODO = s 1/f /f 1 1 s = 1 + s f 0 1 s f 2 2s + s2 f 1 s f s2 f 2 which is a multiplication of the transfer matrix of each element of the FODO cell. The stability condition (periodic motion) for a FODO is related with the trace of this matrix, T r(m F ODO ) < 2 (2.26) From this condition we can infer that the drift space s should be less than 2f. 29

45 2.7.3 Lithium Lens The most important characteristic of a lithium lens is the ability to focus in both transverse planes at the same time. Lithium is chosen because it is the least dense conductor, minimizing particle losses and multiple scattering. The lithium lens is basically an electromagnetic lens, in which a uniform axial current I flows though a solid lithium cylinder along its ẑ axis generating a magnetic field B(r) whose strength is directly proportional to the radial coordinate r, and whose direction follows concentric rings about the conductor in the ˆφ direction, B(r) = µ 0Ir = Gr (2.27) 2πR2 where G is the gradient field [T/m] of the lens. By the Lorentz force the field focuses particles to the center at r = 0. Fig shows this characteristic. At the Tevatron 120 GeV protons Figure A lithium lens collecting particles and orientating them horizontally. hit a small spot on a Nickel target. The Lithium Lens collected the antiprotons and the rest of the particles produced by the proton beam hitting the target. The focal length can be calculated using the equations 2.22 and 2.23 to obtain, f[m] = p[gev/c] 0.3G[T/m]l[m] (2.28) 30

46 Now, the acceptance angle of the lens for the particles collected is given by, α[rad] = R f (2.29) Beam Separation Devices Beam separation should be made with minimum beam loss and disruption of emittance. Some specialized devices are used for this purpose. Among them are the electrostatic and magnetic septa. An electrostatic septum (Fig. 2.25) is used to split a particle beam Figure Beam deflection produced by an electric septa. using electrostatic fields. Two electric fields of opposite direction are created by an array of grounded wires placed in the center. Thus, when the particle beam goes though the septum, it is separated in opposite directions. If only a portion of the beam is required to be extracted, a modified electrostatic septum is used as is shown in Fig This consists of thin foils that forms a ground plane that separates two field regions between the electrode and the field free region for the circulating beam. The beam is divided into two parts, in which the part that passes in the field region is extracted. From the Lorentz force F = qe, and taking the electric field in relativistic form, the force is given by, F z = d dt γmv z (2.30) 31

47 Figure Electrostatic septum used to extract one part of the beam [26]. then, γmv z = qet (2.31) Now, solving for z, z = qe 2γm t2 (2.32) using that E = V/g (where V is the voltage and g the gap width) and t = L/βc, the vertical deflection z (Fig. 2.25) becomes, z = qv L2 (2.33) 2γgβ 2 m 0 In terms of the deflection angle [27], using small angle approximation θ = z/l, we have that θ = V L 2γgβ 2 m 0 (2.34) or θ[rad] = E[V/m]L[m] p[gev/c] 10 9 β (2.35) where the mass m 0 is in ev units. Among the typical technical values for an electrostatic septum are: range length m, gap width mm, septum thickness 100 mm, voltage up to 300 kv and electric field up to 10 MV/m [26]. 32

48 Figure DC Magnetic Septum. The beam is separated into two parts, one enters in the field region B and the other part continues without change in the no field region. Regarding magnetic septum, four types are widely used: Lambertson, Eddy current, pulsed, and DC magnetic septum. All of them have two regions or apertures, one region with a magnetic field produced by a dipole to deflect the beam, and the other a field free region. Fig shows the form of a DC magnetic septum. The current coils form the magnet to produce the magnetic field in the region where the beam is extracted. For this configuration, the magnetic field is given by, B = µ 0I g (2.36) where µ 0 = 4π 10 7 T m/a is the vacuum permeability constant, I the current, and g is the gap width of the field region. Typical parameters values for this septum are: current between 0.5 and 4 ka, septum thickness from 6 to 20 mm, density current of 85 A/mm 2 and gap width of 25 to 60 mm [26]. 2.8 Radio Frequency Cavity The radio frequency (RF) cavity provides a source of Electromagnetic Field for beam acceleration, deceleration, bunching, and debunching. Basically, it is a region enclosed by 33

49 conducting walls (Fig. 2.28) where electromagnetic waves become resonant. These electro- Figure Radio Frequency Cavity. Source: [28]. magnetic fields are solutions to the wave equation, ( c 2 t ) E = 0 (2.37) 2 H where the boundary conditions or the fields at the surface are, ˆn E = 0, ˆn H = 0 (2.38) where ˆn is the normal vector in the surface. These boundary conditions allow no tangential Figure Electric and magnetic fields in a cavity. The electric field accelerates or decelerates the particles according to their arrival time. 34

50 electric field and no normal magnetic field at the walls of the cavity. An RF cavity provides a longitudinal electric field for acceleration. Thus, particles arriving earlier or later will be accelerated less o more so that they reach the reference energy of the ideal particle (see Fig. 2.29). 2.9 Beam Simulation Programs There are various programs used in the analysis of particle beam and charged particle transport. They are designed to study the trajectory and behavior of these particles by using sophisticated tools to simulate components used in the particle accelerators. One of those simulation programs is called G4beamline [29], which is used in this work. G4beamline is a particle tracking program, which models the behavior of particle beams, for example, when going through magnetic elements, RF cavities, target, etc. These elements are created using geometric forms, varieties of materials, and electromagnetic fields. A nice advantage of this simulation program is the output GUI environment, which shows all the elements used and the beam position. The geometry of the simulation can be verified through the visualization of the elements used in the simulation. For example, Fig shows a basic simulation of a beam going through two separated quadrupole magnets to focus the beam in a specific region. The data of interest can be stored to be plotted or Figure Simulation example in G4beamline. A flat beam goes through two quadrupole magnets which focus the beam in a specific region [30]. 35

51 analyzed. These data include position, momentum components, beam sizes, etc., for a given position along the horizontal axis (z). Another simulation program widely used is MAD -X [31] (Methodical Accelerator Design), which is also created to study beam dynamics in the design of accelerators. It also includes a large variety of elements to be simulated with the particle beam. Parameters such as beam size, beta values, dispersion, and other optics parameters are calculated. This program is able to study the behavior of beam size along its path through magnetic devices. For example, Fig shows the MAD -X output plot for the simulation of the CMS inner Figure MAD -X Betatron Function Plot for the CMS Interaction Region. quadrupole system (section ). This plot shows the behavior of the components of the Beta function (which is related to the beam size) having the minimum value in the center, which represents the interaction point of the beams coming from opposite sides. 36

52 CHAPTER 3 3 PROTON-ANTIPROTON COLLIDER REMARKS In this chapter we present some advantages that proton antiproton colliders have with respect to proton-proton colliders. Antiprotons have been used in the past at CERN [18, 32], Fermilab [33 35], and GSI Darmstadt [36, 37]. Also, the SSC (Superconducting Super Collider) Central Design Group [38] presented studies which examined the option of a p p collider ring at the SSC Super Collider in Texas. A prime motivation has always been that production cross sections are often higher for producing high mass states in p p collisions. Many high mass states are created through q q processes. The accelerator can be operated at lower luminosity generating fewer events per beam crossing. Detectors operate with lower events rates where they function more effectively. These reasons all lead to the conclusion that there is decisive advantage in choosing a p p collider over pp colliders for many new high mass physics searches. 3.1 Cross Section for Higher Masses in pp and p p Collisions The rate of event production in a collider will be proportional to the collider s luminosity L and particle production cross section σ. The cross section σ is proportional to the probability of an event or reaction to be created in a collision. It has units of area (cm 2 and barns), where 1 barn (b) = cm 2. N s = L σ (3.1) The cross section for producing high mass events, indicating new physics, will be on the order of tens of femtobarns (10 15 b). At LHC energies, the inelastic cross section for 37

53 production of ordinary particles is of order 85 milibarns (10 3 b). At a luminosity L = cm 2 s 1 collider the rate of producing ordinary events is an overwhelming cm cm 2 s 1 = s 1. In a typical beam crossing time of 25 ns, typically so-called pileup interactions will take place. This all leads to the importance of operating the accelerator at the minimum possible luminosity in order to achieve physics goals. Fig. 3.1 shows the Higgs boson production cross sections in pp collisions in terms of the Higgs mass for different processes. There it can be seen the gluon fusion (gg) process dominates the lighter Higgs production in pp collisions up to the 1 TeV range. The q q part of the total cross section will be more important at higher masses, scaling with mass of the object M over center of mass collision energy M/ s. The cross section to produce high mass objects in p p collisions can be of order 10 times higher than it is for proton-proton collisions [39, 40]. Figure 3.1. Cross sections in term of the mass for the Higgs production at E cm =7 TeV [41]. Because of the typically higher cross sections at proton anti-proton machines the p p collider can achieve sensitivity for high mass states while running at a lower luminosity L. At pp colliders, running at higher luminosity, increases detector pileup and synchrotron radiation in the superconducting magnets and the vacuum system. This has adverse affects on the 38

54 accelerator design and operation of detector systems. As beam currents are increased more synchrotron radiation is produced in the superconducting magnets in the form of unwanted heat. Several studies of cross sections are available for producing new physics in pp machines relating to the LHC and upgrade era. In some cases the physics generators for predicting these processes have not fully been verified in the 100 TeV region, as higher level perturbative Feynman diagrams become important. The cross section for p p collisions is greater than in pp collisions for higher masses, as in shown in Fig There it can be seen that the cross section for particles similar to the top quark production is greater in proton-antiproton collision than in proton-proton collision as mass increases. Figure 3.2. Top-like Anti-top-like Cross section production as a function of the mass using pp and p p collisions [39]. As fewer detailed calculations were available for guidance in the design of our 100 TeV p p collider, we proceeded with our own investigations. Several simulations program packages are available to generate hard events, showering, and hadronization (quarks and gluons). These Monte Carlo programs are used in high energy physics to study the properties 39

55 of the process in which the particles are generated by colliding two incoming particle beams. The processes for high mass states are produced as a function of their corresponding cross sections. We can compare the simulation results with existing real data from the experiments or future particle colliders. Some generators used in particle physics are hadronic event generators, in particular Pythia, Herwig, Isajet, and Sherpa. Other multipurpose parton level generators are Madgraph5 and Whizard. We use the generators Madgraph5 [42] and Pythia6 [43] which are currently very commonly used in particles physics. MadGraph5 [42] is a multi-purpose matrix element generator program for High Energy Physics, written in Python, to simulate and generate events as particles decays and scatterings. It gives useful results as the four momentum vectors (p x, p y, p z, E), cross sections, and all Feynman diagrams for the process generated. It also provides a variety of tools for manipulation and analysis. It generates a lhe (Les Houches Event) output file, which contains the process generated, information as to the number of events, the energy of each beam, the beam type (proton, antiproton, photon, etc.), particle masses, and other relevant parameters. Also it gives a complete list of all particles in the process as the momentum components (p x, p y, p z ), energy, and particle mass. This file is used to plot kinematic distributions as mass, momentum, angular variables, etc. Pythia6 [43] is second event generator which is useful for hadronic processes in collisions involving proton-proton (pp), proton-antiproton (p p), positron-electron (e + e ), electron-proton (e p) and muon-muon (µ + µ ) beam interactions. The latest version of the program is written in the C++ programing language, previous versions were written in Fortran. Pythia has built-in over 200 Standard Model (SM) and Beyond Standard Model (BSM) subprocesses. Our new 100 TeV collider is designed to search for physics beyond the standard model (BSM). Several new particles are predicted by unified theories. We focused on the heavy W boson, which is a massive version of the standard model W boson. This predicted boson is considered to have a mass at the TeV scale, and be produced through q q collision. Fig

56 shows the Feynman diagram for W production from q q and qq collision. There it can be seen that antiquarks for W production can come directly from an antiproton rather than indirectly from gluon splitting in proton-proton collisions. The anti-quarks which are present in the p represent a significant advantage in using p p colliders. Figure 3.3. Feynman Diagrams for W production from a) q q collision, b) qq collision. We programmed the two event generators, Madgraph5 and Pythia6, to obtained the W cross section for different W masses, using proton-proton and proton-antiproton collisions with a center of mass energy of 100 TeV. These calculations are the first that we know of published with the Madgraph and Pythia generators for p p collisions. The results, using Madgraph, are shown in Fig They show that the cross section for p p collisions is greater than in pp collisions for higher masses, as expected. See Fig As the W mass increases the production cross section obtained with p p collisions grows as compared with pp collision, becoming about 10 times larger at 40 TeV/c 2. The procedure was repeated using the Pythia event generator. The results are shown in Fig Again it can be noticed how the W cross section is greater in p p collisions as the mass increases. The difference in absolute cross sections from those obtained with Madgraph and Pythia generators at higher masses is due to the difference in higher order Feynman amplitudes considered in each generator. However for masses less than 20 TeV/c 2 the cross section values are close in both programs. Summarizing, the great advantage of having higher cross sections for W and other high mass states is that it permits a 100 TeV collider with less detector pileup. Pileup 41

57 Figure 3.4. MadGraph results for W Boson production cross section as a function of the mass using pp and p p collisions with a E cm = 100 TeV. Figure 3.5. Pythia results for W Boson production cross section as a function of the mass using pp and p p collisions with a E cm = 100 TeV. decreases as antiprotons are distributed into more bunches. There is a limit to this as the number of protons per bunch must stay constant to keep the luminosity constant, and synchrotron radiation rises with the number of protons. Next we consider the substantial advantages in running the accelerator at lower beam current with regard to lowering syn- 42

58 chrotron radiation levels. 3.2 Synchrotron Radiation in High Energy Colliders As noted the higher cross sections particles production (p p collider) allow the collider to be run at lower beam currents and luminosities. Synchrotron radiation (SR) in the collider s superconducting magnets and vacuum system, can cause severe radiation damage to materials and cause unwanted heating. We can estimate the power that is emitted due to Synchrotron Radiation. Equation 2.12 gives the power emitted per particle, P = c q 2 (βγ)4 6πɛ 0 ρr For example, at the LHC (E = 7 TeV, γ = E/m = 7460, ρ = 2.8 km, R = 4300 m) the SR power for a proton is P = kw. Thus, for a proton beam, which consists of 2808 bunches and protons per bunch, the total SR radiated is 3.9 kw. Now, if the particle energy is increased, the SR power grows as γ 4 /ρr creating a serious limitation to deal with in the design of new high energy (100 TeV) colliders [44]. Table 3.1 shows the parameters and the SR power calculations for a 100 km pp collider [45] and for the 270 km p p collider proposed is this work. Table 3.1. Synchrotron Radiation (SR) for a 100 km pp and 270 km p p circumference colliders. γ = E/m = 53, TeV beam energy. R B ρ Packing SR/proton Bunches Particles SR/pipe Beam SR/meter m T m Fraction kw /beam /bunch kw Pipes W/m pp 15, , , p p 42, , ,800 20/ It is important to highlight that the SR Power per meter is 13 times lower for the 100 TeV p p compared with the pp collider, because higher production cross sections of 43

59 high p T particles allow lower beam currents and because the tunnel circumference is larger. Furthermore, a p p collider only requires one ring instead of the two needed for a pp collider. The same magnets are shared by both beams because of their opposite charge, reducing costs. All reasons above are advantages of a high energy proton-antiproton collider. 44

60 CHAPTER 4 4 ANTIPROTON CAPTURE In the design of a new cm 2 s 1 high luminosity proton-antiproton collider increasing the number of available antiprotons is the crucial factor. The Fermilab Tevatron had a powerful antiproton source, which cooled about p/h in the Debuncher ring and p/h in the Accumulator ring. In the Tevatron s antiproton source the momentum was 8.9 GeV/c ± 2%, yielding a 2% momentum acceptance into the next cooling stage. A large number of antiprotons were rejected because of the low acceptance. This chapter presents the viability of being more efficient and collecting more antiprotons, rather than just producing more of them from a Fermilab -like target station. Our goal is to increase the momentum acceptance from 2% to 24%, with 12 more antiprotons collected. 4.1 Luminosity Requirements As a starting point, we take as reference the Tevatron collider (TEV). We can estimate the needed increase in luminosity L, equation 2.7, of the new 100 TeV collider by scaling from Tevatron parameters of: luminosity L T EV = cm 2 s 1, energy E T EV = 0.96 TeV, and circumference l = 6.28 km. L = L = E E T EV l T EV l β T EV β L T EV 50 TeV 6.28 km TeV 270 km 1032 cm 2 s 1 L = cm 2 s 1 The β factor 2 comes from the reduction of β = 28 cm at the Tevatron to a β = 14 cm at the new collider. With basic dynamical changes in the new collider size and energy the luminosity is increased by a factor of 2.4 over the Tevatron. However, to achieve a luminosity of cm 2 s 1, approximately 12 more bunches are needed. 45

61 The number of antiprotons available for the collisions is given by the event or burn rate, p burn rate, which depends on the total proton/antiproton cross section and the luminosity. At high center of mass (cm) energy (E cm 200 GeV) the total annihilation cross section is the same for pp and p p collisions [46]. For E cm = 100 TeV, the total cross section is σ = 153 mbarn [47]. The antiproton burn rate will be p burn rate = σl = /h. The Fermilab Debuncher cooled a peak of p/h [48]. We then estimate that to keep up with the p burn rate, 12 more antiprotons are needed. At the Fermilab antiproton source a large number of antiprotons were rejected because of the modest momentum acceptance. We adopt a strategy of keeping the antiproton source fixed, and explore means of collecting more of p s, specifically around 8.9 GeV/c ± 24%. Providing a second Accumulator ring might improve the Accumulator ring stacking rate [49]. At Fermilab, the Accumulator stacked 62% of the Debuncher output. 4.2 Increase in Antiproton Momentum Acceptance At the Fermilab antiproton target station p s were created by hitting an Inconel (a low expansion nickel-iron alloy) target with a 0.1 mm spot beam size of 120 GeV protons, with a optimum production of antiprotons with a momentum range from 8 to 13 GeV/c. The angular distribution of the produced antiprotons is gaussian shaped with sigma [50], σ θ 1.1 mπ (4.1) γ m p where m π (139.6 MeV/c 2 ) is the pion mass, m p (938.3 MeV/c 2 ) is the proton mass and γ is the relativistic boost factor (E/m) of the antiprotons. For example, for 8.9 GeV/c antiprotons the angular distribution has a sigma value of 45 mrad. The effective geometric emittance (phase space area) of the 8.9 GeV/c antiprotons exiting the target is 26 µm (247 µm rms normalized). Now, with reference to the antiprotons momentum, Fig. 4.1 shows the momentum distribution for antiprotons created by a 120 GeV proton beam hitting a tungsten target 46

62 within a production angle of 60 mrad. This plot was reproduced taking as reference Figure 4 of the paper Calculation of anti-proton Yields for the Fermilab anti-proton Source [51], considering that Inconel and tungsten should give similar distributions. The plot follows a Landau distribution function (blue trace) in the important momentum range of 5-18 GeV/c. Thus, the goal is to collect the antiprotons within an approximate momentum range of p = 11.0 GeV/c ± 24% or p = (11.0 ± 2.6)GeV/c, taking 11.0 GeV/c as the central momentum. Figure 4.1. Momentum distribution of the antiprotons produced by a 120 GeV proton beam hitting a tungsten target [51]. In the Tevatron target station, the particles that emerged from the target were focused by a lithium lens. This was a solid cylinder of radius 1 cm and length 15 cm, in which an high 500 ka axial current produced a strong radial gradient of 1,000 T/m. The effective focal length was 20.0 cm. To increase the momentum acceptance of the antiprotons, a system of multiple lenses or a longer single lens might be necessary [52]. To go from 8.9 to 11.0 GeV/c the lithium lens is lengthened from 15 to 18.6 cm. The new focal length for the central momentum of 11 GeV/c is 20 cm. This is calculated using the equation 2.28 from Chapter 2. To measure the effectiveness of the new lens, a G4beamline simulation was performed 47

63 by creating a beam with a Landau momentum distribution (11 GeV/c, σ = 4 GeV/c) (Fig. 4.1), a gaussian angular distribution θ (0, 45 mrad), a uniform azimuthal distribution φ = (0, 2π), and momentum components p x = p sin(θ) cos(φ), p y = p sin(θ) sin(φ), p z = p cos(θ) These parameters simulate the beam coming from the target. The purpose of the lithium lens is to reduce the transverse momentum, p t = p 2 x + p 2 y, of the beam. Fig. 4.2 shows a divergent beam (p = 8.9 GeV/c ± 2%) simulated in G4beamline, as if it was coming out of a target and passing through the lithium lens. The beam is oriented in the horizontal Figure GeV/c± 2% antiproton beam simulation crossing a lithium lens. The plots show the transverse momentum distribution of the beam before entering (left plot) and in the output of the lithium lens (right plot). direction. The transverse momentum of the beam before entering the lens, as well as the 48

64 transverse momentum distribution in the lens output is shown in the same figure. Taking as reference the mean transverse momentum value, p t, this represents a 91% reduction. Similarly, a G4beamline simulation is performed, but using a beam with momentum p = 11 GeV/c ± 24% and crossing the lithium lens of 18.6 cm in length. The simulation is shown in Fig. 4.3 together with the initial and final transverse momentum distribution of the beam. The optimum position to be placed the lens from the target to its center was determined to be 22 cm. Here, the mean value is reduced by 89%. It can be noted that the 18.6 cm lens does a good job of reducing the transverse momentum of a beam with a large momentum spread. Figure GeV/c ± 24% antiproton beam simulation crossing a lithium lens in G4beamline. The plots show the transverse momentum distribution of the beam before entering (left plot) and in the output of the lithium lens (right plot). In the lithium lens, the antiprotons experience scattering and absorption. The ab- 49

65 sorption causes loss and the scattering causes emittance growth. The deflection angle due to the Coulomb scattering [53] is given by, θ 0 = 13.6 MeV z x/x 0 [ ln(x/x 0 )] (4.2) βcp where β = 1, p = 11 GeV/c, z = 1 (charge number) for the incident antiprotons, x is the Li lens length (18.6 cm), and X 0 is the radiation length of the Li (15.5 cm). Substituting these values the scattering angle is 0.41 mrad. βγ = p/m = 11.0/0.938 = Thus, the normalized emittance growth [50], ɛ N = βγr lens θ 0 = 48 µm (4.3) The growth is small when added in quadrature to the initial normalized transverse beam emittance of 330 µm. To separate the antiprotons from the others particles (p, n, π +, etc), a pulsed dipole is located after the lithium lens and separates the particles according to charge. The negatively charged antiprotons are bent by 3 and the other particles are sent to a dump (graphite surrounded by steel) to be absorbed. 4.3 Antiproton Beam Separation and Transport More antiprotons are needed, if luminosity is to be increased. To do this a large momentum spread beam is accepted and then quickly spread into a dozen beams with lower momentum spreads. This is simulated in G4beamline. The simulated antiproton beam coming from the Li lens is dispersed using a 1.5 m long dipole with magnetic field of -1.8 T. Fig. 4.4 shows the momentum vs x position for the initial beam and when the beam is dispersed. Here x(mm) represents the vertical coordinate in the G4beamline simulation. The particles with high momentum experience less deflection. The dispersed beam can be divided by placing an electrostatic septum and two mag- 50

66 Figure 4.4. Momentum vs x position for the initial beam (left plot) and the dispersed beam (right plot). netic septa to increase the separation. The electrostatic portion has a thin septum 100 µm minimizing beam loss, and the magnetic one has a thin septum between 2-20 mm. The beam exiting from the electrostatic septum should have equal or greater deflection than the magnetic septum thickness to minimize any interaction with the material. Fig. 4.5 presents the Figure 4.5. Configuration to divide the beam into two parts. An initial beam with momentum acceptance p = 11.0 GeV/c ± 24% is collected by the Li lens and dispersed by a magnetic dipole to be then divided by a electrostatic septa ES and two magnetic dipoles MS. basic cell to divide the initial dispersed beam into two: An initial beam with Landau function momentum distribution (11 GeV/c, 1.5 GeV/c) 51

67 enters the Li lens and then is spread by a -1.8 T dipole of 1.5 m in length. An electrostatic septum (ES) divides the beam, which is placed in such a way that half is deflected. The parameters used for the septa are: length = 6 m, Electric Field = ±1.0 MV/m, gap = 0.30 m and septum thickness = 0.2 mm. Next to the electrostatic septum a 0.1 T magnetic septum (MS), 3.5 m long, with septum thickness of 4.0 mm is placed to increase the beam separation. This magnet provides a deflection range of mm into the momentum acceptance required. A 3.0 m long magnetic septum, 1.0 T, is placed next to the 0.1 T dipole to allow a greater separation between the divided beam. This provides a deflection range of mm. To transport the beam a FODO cell (26.3 m) is used. This consists of a focusing quadrupole FQ, a drift space and a defocusing quadrupole DQ. The quadrupoles are 0.66 m in length, aperture radius of 1.0 m and field gradients of ± 2.0 T/m. This FODO length is chosen to be equal to the AP2 transport line in the Tevatron. Table 4.1 presents the parameters of the cell which divides the initial beam. The process is repeated to separate the deflected beam into two again, obtaining two beams, and finally each of these beams is separated into three to get the first six beams (Fig. 4.7). To obtain the next six beams, the initial half beam, which is was not deflected is transported to be dispersed using a second -1.8 T dipole. Then, the same configuration is used to obtain the other six beams. To get the beams 10, 11 and 12 the beam is dispersed again to improve the separation in momentum distribution plots. At the end 12 beams are produced as is shown in Fig The momentum distribution of each beam is calculated using G4beamline as soon as a beam is divided. G4beamline provides an output file which contains information, mainly of 52

68 Table 4.1. Parameters of the basic cell to divide the initial beam. Dipole FQ ES MS1 MS2 DQ Unit Magnetic Field B T Field Gradient G T/m Length L m Radius R m Width w m Septum thickness mm coordinates and momentum components of the particles of the beam. For example, Fig. 4.6 shows the distribution in momentum of the initial beam (upper plot) and after it is divided into two (bottom plot). A separation in momentum is observed. There the lower beam (Beam 1) has a smaller mean momentum and the upper beam (Beam 2) a higher mean momentum. The momentum distributions of the final 12 beams are shown in Fig. 4.8, Fig. 4.9, Fig. 4.10, Figure 4.6. Momentum distribution of the initial beam (upper plot) and when it is divided into two (bottom plot). 53

69 54 Figure 4.7. An initial beam with momentum acceptance p = 11.0 GeV/c ± 24%is divided to finally get twelve beams.

70 and Fig There the momenta for each beam can be seen. Twelve different momentum channels are obtained. To calculate the total transmission, the antiproton transmission of all twelve channels are added, and then compared with the transmission of the initial beam (Fig. 4.6, upper plot). The total transmission fraction through all 12 channels is calculated to be 91%, an acceptable result. Figure 4.8. Momentum distribution of the beams 1, 2 and 3. Figure 4.9. Momentum distribution of the beams 4, 5 and 6. 55

71 Figure Momentum distribution of the beams 7, 8 and 9. Figure Momentum distribution of the beams 10, 11 and 12. Table 4.3 presents the mean values of the momentum of each beam together with the width of each distribution, which is calculated with the standard deviation and the mean values of each distribution. To improve the acceptance, sextupoles could be used for chromaticity correction. However this is beyond the scope of this work. 56

72 Table 4.2. Mean momentum value of the 12 beams obtained. Beam p (GeV/c) ± 2.0 % ± 2.1 % ± 2.4 % ± 2.6 % ± 2.2 % ± 2.9 % ± 2.7 % ± 2.0 % ± 2.8 % ± 2.6 % ± 2.3 % ± 1.7 % 57

73 CHAPTER 5 5 ANTIPROTON COOLING In the previous section, it is shown how the initial antiproton beam was dispersed and divided into 12 different momentum channels with a transmission of 91%. Now, because the momentum acceptance into the Debuncher and Accumulator rings is p = 8.9 GeV/c ± 2%, as well as into the Recycler ring, it is necessary to equalize the central momentum of all the 12 beams to that value. We again look to the Fermilab approach. At Fermilab, antiprotons were stochastically precooled in the Debuncher ring during 2.2 s, with transverse emittance (RMS Normalized) reduction from 330 to 30 µm, then sent to the Accumulator ring to be stochastically cooled and stacked. There, the transverse emittance (RMS Normalized) was reduced from 30 to 15 µm. Table 5.1 shows the reduction in emittance and momentum spread in the Debuncher, Accumulator, and Recycler rings. Table 5.1. Fermilab antiproton cooling stages [54]. The normalized rms emittance shown comes from multiplying geometric rms emittance by β γ = p/m = 8.9/0.938 = A modest amount of stochastic cooling is performed in the Recycler ring to prepare for electron cooling in the same ring. Stage Norm. RMS Transverse Momentum Spread Emittance ε N(x,y) (µm) p/p (MeV/c) Debuncher Entrance 330 ±200 After Phase Rotation ±9 Debuncher Exit 30 ±4.5 Accumulator Exit 15 ±9 Recycler Exit 2 ±1.8 It is known that the stochastic cooling time scales linearly as the number of parti- 58

74 cles [20, 55], τ N 10 8 s. (5.1) Thus, we take a simple approach, to cool 12 the number of antiprotons, we implement 12 independent cooling channels. Two configurations are proposed. The first choice consists of implementing two Accumulators and one Debuncher for each of the 12 independent systems. The second choice is to use only Debuncher rings, two for each independent system. The total would be 24 Debuncher rings. Finally an electron cooling ring follows either of these configurations. In the second option, stacking is done with electron cooling. 5.1 Debuncher-Accumulator Rings In choice one, to cool 12 the number of antiprotons, 12 independent cooling systems would be implemented as is shown in Fig Each Debuncher ring phase rotates (section Figure 5.1. To cool 12 more antiprotons, 12 independent cooling systems would be implemented. Two accumulator rings can keep up with one p/h Debuncher output rate ) the beam to lower the momentum spread, ramps the beam central momenta up or down to 8.9 GeV/c, and stochastically cools. Each Debuncher alternately outputs antiprotons to 59

75 each of two associated accumulator rings. Each system would have a Debuncher/momentum equalizer, which would use RF cavities to reduce the 2% momentum spread by decelerating fast antiprotons and accelerating slow ones. In addition, the central momenta of all 12 channels would be equalized. The Debuncher would alternately feed two Accumulator rings. At Fermilab the single Accumulator ring cooled p/h. A second Accumulator ring doubles the time in the deposition orbit and reduces required stack sizes. Two Accumulator rings may be able keep up with one p/h Debuncher. In addition, a single electron cooling ring could follow the stochastic cooling. 5.2 Debuncher Rings Twenty four Accumulator rings may be difficult to build and operate. Thus, this second option of a cooling system is presented with only Debuncher rings as is shown in Fig Figure independent cooling systems using only Debuncher rings. Alternatively, bunch coalescing might be done with electron rather than stochastic cooling. In the second option each of the 12 channels would have two Debuncher rings. Each Debuncher receives the respective quantity of antiprotons with a time gap of 2.2 s, but the 60

76 Figure 5.3. Antiprotons are sent alternatively from the target to each Debuncher to increase the cooling time from 2.2 to 4.4 s, allowing emittance (RMS, Normalized) reduction from 330 to 3 µm. antiprotons would be stay 4.4 s in the respective Debuncher (Fig. 5.3). Thus, the emittance (RMS, normalized) is reduced from 330 to 30 µm during the first 2.2 seconds and from 30 to 3 µm during the next 2.2 s. It will produce more emittance reduction than is obtained with an Accumulator ring. It will not stack bunches. The accumulation and stacking of antiprotons was provided by the Accumulator ring at Fermilab. Since this new proposed cooling system does not include Accumulator rings, stacking would be performed in the electron cooling ring. Antiprotons must be sufficiently pre-cooled for electron cooling to work. The velocities of the antiprotons and electrons must be close to each other. 5.3 Electron Cooling System In addition to this new cooling system, a single electron cooling ring could follow the antiproton cooling. Electrons can cool large numbers of medium emittance antiprotons in one ring [56, 57]. In 2005 electron cooling was introduced at the Recycler ring at Fermilab with the purpose of providing additional cooling to the antiprotons. An important consequence of this was an increase in luminosity [58]. The Fermilab electron cooling system is shown 61

77 in Fig An 8 m high electrostatic generator supplies an electron beam (produced by a thermionic cathode gun) with kinetic energy of 4.3 MeV, current of 0.5 A, and beam power of 2.15 MW. The 20 m cooling section is incorporated into the Recycler ring. In that section the 4.3 MeV electrons and 8.9 GeV antiprotons experience Coulomb interaction so that fast antiprotons will slow down and the slow ones will speed up. The warmer antiprotons cool down and the cooler electrons get warmer. This cooling section is composed of 10 solenoid modules, each 2 m long, with low magnetic field (0.01 T). Finally, the electrons are returned back through a separate line. The electron cooling system parameters are summarized in Table 5.2. Figure 5.4. Fermilab Electron Cooling System [59]. Table 5.2. Electron Cooling System Main Parameters. Value Unit Electron Beam Energy 4.3 MeV Beam current 0.5 A Voltage ripple, rms 500 V Cooling Section Length 20 m Solenoid Module Field 0.01 T Beam radius 6 mm Angular Spread 0.2 mrad Energy Spread 300 ev 62

78 This cooling system, decreases the longitudinal emittance from 100 ev-s to 50 ev-s. This emittance reduction is reached in 30 minutes for stacks up to antiprotons [60]. With either of the two cooling systems described in the preceding sections, around antiprotons per hour are sent alternately by each Accumulator or Debuncher to the electron cooling ring. Thus, in 1 hour the electron cooling ring will receive antiprotons. The electron cooling time is independent of the number of particles being cooled, but is proportional to γ 2 (where γ = E/m) and the ring fraction occupied by the electrons. Consequently, if we keep the same electron ring size and the total antiproton energy is reduced by a factor of three, from 8.94 GeV to 2.98 GeV, the cooling rate increases by a factor of nine. Therefore, the electron cooling time would decrease from 30.0 to 3.3 minutes. The parameters of the antiprotons in the ring, where the 20 m electron cooling section is inserted, are shown in table 5.3. Table 5.3. Electron Ring Main Parameters. Value Unit Circumference 3300 m Energy 3.0 GeV γ rel 3.2 β rel 0.95 β function 20 m ε N (RMS) 1.5 µm Beam Size (σ) 3 mm In the absence of 24 accumulator rings, all the antiprotons bunches would be stacked in the single electron cooling ring. The 8.9 GeV/c antiproton beam started out with a momentum spread of 2% or about 200 MeV/c. Table 5.1 shows the progression of antiproton cooling at Fermilab. Only a small amount of additional stochastic cooling had to occur in the Recycler ring before electron cooling could commence. The Debuncher ring had two longitudinal and four transverse stochastic cooling systems. Antiprotons at Fermilab were cooled from 330 µm to 30 µm in the Debuncher ring. Phase rotation alone in the Debuncher 63

79 was almost enough to lower the momentum spread to the level needed for electron cooling. The Fermilab electron cooling ring reduced longitudinal emittance by a factor of two in 30 minutes. In thirty minutes the system in this paper would produce 9000 bunches, which is roughly the number of antiproton bunches in the machine. They would just need to be coalesced with bunches produced in previous half hour intervals. The current system might be enough. However, electron cooling is proportional to 1/γ 2. Reducing the total antiproton energy by a factor of three from 8.94 GeV to 2.98 GeV decreases γ by a factor of three and increases the cooling rate by a margin of nine. The electric field arising from space charge is given by [61] E s = E w eg 0 λ 4πɛ 0 γ 2 s (5.2) where E s and E w are the electric fields at the beam pipe center and wall (see Fig. 5.5), e = coulombs, g 0 = 1 + 2ln(b/a) is a geometry factor, a is the beam radius, b is the beam pipe radius, ɛ 0 = farads/meter, and λ is the antiproton line density. The Fermilab Recycler had four RF cavities and a combined total accelerating gap voltage Figure 5.5. Electric fields at the beam pipe center and wall of a circulating beam. of 2 kv [62]. This may need to be increased to 36 cavities and 18 kv to control space charge, 64

80 if the ring energy were lowered by a factor of three. 5.4 Recycling of Antiprotons in the Collider Ring The production of antiproton beams is more difficult than proton beams, thus maximal conservation of antiprotons is important. It will be most efficient to recycle p s to conserve, rather than dumping them at the end of runs. Antiprotons in the collider ring can be recycled without leaving the ring. During the CERN Sp p S ramping run [63, 64] beam energy was ramped as collisions occurred. Figure 5.6. Snap Bunch Coalescing. (a) A group of bunches are centered at low frequency and their momentum spread is reduced. From (b) to (c) the bunches are rotated for 1/4 of a synchrotron oscillation period at low frequency and then captured at high frequency. The momentum spread increases and the bunches are captured in a single bucket. New antiprotons would be joined to depleted bunches in the collider ring. This technique is called snap bunch coalescing, in which two bunches are combined to form a larger bunch with more antiprotons. This process is shown in Fig The horizontal axis corresponds to the azimuth angle (φ) in the ring or time spread, and the vertical axis is the energy 65

81 offset with respect to the ring energy. Generally two radio frequency (RF) systems operate with different frequency. The bunches are rotated for 1/4 of a synchrotron oscillation period at low frequency (2.5 MHz) and then captured at high frequency (53 MHz) [65]. Finally new and old antiprotons bunches would be completely coalesced with synchrotron damping (section 2.6), which decreases transverse emittance. Synchrotron damping also compensates for the loss of antiprotons from collisions so that the luminosity can be maintained during a run [5]. 66

82 CHAPTER 6 6 COLLIDER DESIGN AND PARAMETERS 6.1 Collider Layout For the construction of the 100 TeV p p collider, two possible rock strata are considered: Fermilab (Chicago, IL) dolomite and Dallas (Texas) chalk. Driving the decision on location are the considerations that Fermilab would have the advantage of existing infrastructure and Texas would have lower tunneling costs. Fig. 6.1 shows the proposed configuration for the 100 TeV p p collider. The components are described below: An upgraded 800 MeV super-conducting Linac [66], which Fermilab has proposed to provide megawatt proton beams for muon and neutrino experiments. The 190 m long Linac would accelerate H ions to an energy of 800 MeV before passing them through a thin carbon foil, as was done previously at low energy, to remove the electrons. This allows charge exchange injection into the Booster and avoids a kicker magnet. More 800 than 400 MeV protons can be injected into the Booster. The Booster accelerates the 800 MeV protons to an energy of 8.94 GeV. The Booster would run at 15 Hz. The 120 GeV ring receives the 8.94 GeV protons to be accelerated to 120 GeV energy, which are sent to the antiproton source to produce the antiprotons. For antiproton production, a Fermilab-like antiproton source is adapted to the new collider. This will collect 12 more antiprotons with the switchyard dipole septa, where the antiprotons are dispersed and separated into 12 different momentum channels. For antiproton cooling 12 sets of rings are implemented. 67

83 Figure TeV proton-antiproton collider (not to scale). An intermediate energy ring between 120 GeV and 22 TeV is not shown. Bunch stacking in the single electron cooling ring might replace the 24 Accumulator rings. A bit of additional transverse cooling would have to be coaxed out of the Debuncher rings to allow electron cooling. The electron cooling ring receives and provides additional cooling to the antiprotons coming from the antiproton source. The 20 m long electron cooling system is inserted inside the 3 GeV ring, which would be 3.3 km in circumference. In the 120 GeV ring, both protons and antiprotons are accelerated to 120 GeV before transfer to the 22 TeV Injector. An intermediate energy ring may also be useful. The 22 TeV Injector accelerates the protons and antiprotons to 22 TeV. This energy would be reached using 2 T magnets in the 270 km ring tunnel. 68

84 Finally, the 50 TeV collider ring will accelerate the protons and antiprotons from 22 TeV to 50 TeV to collide them with a 100 TeV center of mass energy. The 50 TeV energy would be reached using 4.5 T magnets in a 270 km circumference ring. Both 22 and 50 TeV rings share the same tunnel. The relatively inexpensive 2 T superferric magnet injector would be built first and used as a collider. The 4.5 T NbTi magnets would be an upgrade. Collisions would include p p and p P b. Using both the 2 T and 4.5 T rings would allow asymmetric P b P b collisions. Lepton colliders might also share the tunnel [39, 40, 67 78]. In Illinois, the 270 km ring could be annexed to the Tevatron at Fermilab as is shown in Fig In Texas, the 270 km ring could be connected to the partially existing SSC Figure 6.2. Possible scenario to construct the 270 km ring in Illinois connected to Fermilab. An engineering study has been done for a 233 km ring at Fermilab [79, 80]. Map data: Google. 69

85 (Superconducting Super Collider) [81] ring tunnel. Of its initial 87 km design, 45% was bored. The goal of this tunnel was to provide proton-proton collisions with a center of mass energy of 40 TeV, much higher than the Large Hadron Collider. The project was canceled in 1993 due to the higher costs (around $12 billion) compared with the initial $4.4 billion budgeted cost [82]. The increase in cost was partially due to the magnets (6.6 T) that were in development. This geographical zone has the advantage of a homogeneous soft rock composition allowing rapid and cheaper tunnel boring, which is a way to reduce costs. Fig. 6.3 shows the 270 km ring on a map. Figure 6.3. Layout of the 270 km ring around Dallas, Texas [83]. Map data: Google. The 270 km ring would be difficult to build at CERN due to the cost of tunneling under the Jura mountains. Recent analysis does consider the construction of a 100 TeV collider FCC (Future Circular Collider) with a km ring circumference in the Lake Geneva valley as shown in Fig This would be a positron-electron (e + e ) and a proton- 70

86 proton collider. For this km ring, geological conditions are being evaluated. Risks and costs are being considered [84]. Figure km tunnel to host a 100 TeV pp collider at CERN in the Lake Geneva valley. Image credit: CERN. 6.2 Tunneling Tunneling cost depends on geology. Table 6.1 shows the cost per meter estimates for boring 4 m diameter tunnels in three different locations. These values are taken from M. Breidenbach and W. Barletta, ESS-DOC-371 [85] to estimate the total cost of a 270 km tunnel. At CERN the tunnel is limited to km due to the French Jura mountains. A tunnel larger than 100 km would cost much more than $39,000/m. For this reason the total cost for a 270 km tunnel at CERN is not presented in the table. Now, comparing the total cost for tunneling at Fermilab and Texas, the cost difference is a factor of 2.5. Texas chalk is easier to bore than Illinois dolomite. The LEP tunnel construction project took 4 years, beginning in 1985 and finishing in Three tunneling machines were used to bore the 4 m diameter tunnel. The average 71

87 Table 6.1. Comparison between tunneling cost for three different locations considered for a 270 km collider ring [85]. Cost/m 270 km tunnel CERN (Molasse/limestone) $39, km limit FERMILAB (Dolomite) $15,000 $4 billion Texas(Chalk/marl) $6,000 $1.6 billion bore rate per tunneling machine was approximately 5 meters/day. The three tunnels that compose the channel tunnel between France and the UK is each 50 km long. The project took 6 years using eleven tunneling machines. All this information is shown in Table 6.2, along with the calculation of the volume of rock removed. The channel project consisted of two 8 m diameter tunnels plus one 4 m diameter tunnel. From this, we can estimate that the rock removed was million m 3 /year per machine for LEP and million m 3 /year per machine for the Channel Tunnel. For a 270 km tunnel, 3.4 million m 3 of rock would have to be removed. However, rock in Texas is faster to bore; 40 m/day based on SSC tunneling rates [5]. Thus, it would take about 4.6 years using 4 tunneling machines, even better, 3.7 years using 5 tunneling machines. Fermilab has relatively constant dolomite layers. For a 4 m diameter tunnel the average advance rate for a tunnel boring machine is about 20 m/day [86]. Thus, it can be estimated that using 8 boring machines the tunneling time is roughly 4.6 years. Table 6.2. Tunneling-time estimate. Length Volume of rock Time Tunneling (km) (million m 3 ) (years) Machines LEP Channel Tunnel Tunnel (Illinois) Tunnel (Texas)

88 6.3 Main Dipole Magnets In a collider the dipole magnets represent a large budget item. The main LHC magnets are located in the 27 km main ring with a packing fraction of 66%, which gives a bending radius of 2.8 km. According to the equation 2.17 (from chapter 1), ρ[m] = p[gev/c]/0.3b[t], the magnetic field is 8.3 T for an energy of 7 TeV. These twin bore magnets are made of Niobium-Titanium (NbTi) superconducting material running at a temperature of 1.9 K. Fig. 6.5 shows a single aperture, of the LHC main dipole magnet, of the two required for the two beams traveling in opposite direction for the collision. Two layers of NbTi cable Figure 6.5. LHC Main Dipole Magnet. There are two cosθ layers [87]. are distributed to form a cos θ structure. The dipole is 14.3 m long, it operates at 1.9 K and the total current for a 8.3 T magnetic field is 11.8 ka. The LHC required 1232 main dipoles, which represented a total cost of $660 million. The cost of each dipole magnet was $0.5 million [88]. Furthermore, the LHC dipole magnet cost is about 3 times more than its superconductor. A 100 km collider with E cm = 100 TeV requires 16 T magnets, which would need Nb 3 Sn material and its production is still under study [89]. A better balance between magnet and tunneling costs may be found at lower magnetic fields. Stored magnetic field energy decreases linearly with ring circumference. A 100 TeV proton-proton collider in a

89 km tunnel around Dallas, Texas using 4.5 T dipole magnets has been proposed [83]. These magnets use superconducting NbTi cable in conduits as is shown in Fig Twenty turns of cable make up each dipole winding. The magnet operates at 4.5 K. These 4.5 T magnets use about half as much NbTi conductor per Tesla/meter as 8 T cos θ LHC magnets. Fig. 6.7 shows the magnetic configuration of the dipole. Figure T superferric dual bore dipole magnet [5]. A pp collider would only require one bore. Figure T superferric dual bore dipole magnetic design [5]. A pp collider would only require one bore. For the 100 TeV proton antiproton collider, the energy of the Injector would be 22 TeV. Using 2 T superferric, iron dominated magnets, the packing fraction would be 86%. The Injector Ring would share the same 270 km tunnel as the collider ring. These superferric 74